Backlund transformations and the Atiyah-Ward ansatz for non-commutative anti-self-dual Yang-Mills equations

We present Backlund transformations for the non-commutative anti-self-dual Yang Mills equation where the gauge group is G = GL(2), and use it to generate a series of exact solutions from a simple seed solution. The solutions generated by this approach are represented in terms of quasi-determinants. We also explain the origins of all the ingredients of the Backlund transformations within the framework of non-commutative twistor theory. In particular, we show that the generated solutions belong to a non-commutative version of the Atiyah-Ward ansatz.